Estimation of parameters in population models for Schizosaccharomyces pombe from chemostat data

The integro-differential growth model of Eakman, Fredriekson, and Tsuehiya has been employed to fit cell size distribution data for Schizosaccharomyces pombe grown in a chemostat under severe product inhibition by ethanol. The distributions were obtained with a Coulter aperture and an electronic system patterned after that of Harvey and Marr. Four parameters—mean cell division size, cell division size standard deviation, daughter cell size standard deviation, and a growth rate coefficient—were calculated for models where the cell growth rate was inversely proportional to size, constant, and proportional to size. A fourth model, one where sigmoidal growth behavior was simulated by two linear growth segments, was also investigated. Linear and sigmoidal models fit the distribution data best. While the mean cell division size remained relatively constant at all growth rates, standard deviation of division size distribution increased with increasing holding times. Standard deviation of the daughter size distribution remained small at all dilution rates. Unlike previous findings with other organisms, the average cell size of Schizosaccharomyces pobme increased at low growth rates.     

Kinetic study of hybridoma cell growth in continuous culture. I. A model for non-producing cells

The kinetic behavior of a nonproducing hybridoma clone AFP-27-NP was investigated in continuous culture under glucose-limited conditions. A total of more than 21, 000 h of cultures were operated at dilution rates ranging from 0.01 to 0.06 h(-1). The viable cell concentrations, dead cell concentrations, and cell volumes all varied with the dilution rate. A steady-state model was developed based on the biomass concentration and the glucose concentration. The specific growth rate as a function of glucose concentration is described by a model similar to the Monod model with a threshold glucose concentration and a minimum specific growth rate incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. A death rate is included in the model which is described by an inverted Monod-type function of glucose concentration. The yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper region of specific growth rates. No maintenance term for glucose consumption was needed; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepted the specific growth rate axis at a value close to the minimum growth rate. The values for the model parameters were determined from regression analysis of the steady-state data. The model predictions and experimental results fit very well.     

Optimization of process parameters by response surface methodology and kinetic modeling for batch production of canthaxanthin by Dietzia maris NIT-D (accession number: HM151403)

Dietzia maris NIT-D, a canthaxanthin producer, was isolated during routine screening of pigment-producing bacteria. Response surface methodology was applied for statistical designing of process parameters for biomass and canthaxanthin production. The effects of four process parameters (considered as independent variables), namely temperature (10-30?°C), pH (4.75-5.75), shaker speed (75-135?rpm) and percentage inoculum (0.5-2.5?%) on the biomass and canthaxanthin yield (considered as dependent variables) were studied. As much as 122?mg?L(-1) of canthaxanthin was obtained when Dietzia maris NIT-D was incubated for 120?h at 25?°C and 120?rpm, initial pH and percentage inoculum being 5.5 and 2?% respectively. The pigment yield is the highest reported till date, with Dietzia maris as the test organism. The maximum biomass yield was 7.39?g?L(-1) under optimized process parameters. The predicted values were also verified by validation experiments in 5-day fermentation. Different mathematical models were used to describe growth and production, considering the effect of glucose in batch mode. The kinetic constants were calculated by fitting the experimental data to the models. Cell growth was inhibited beyond a glucose concentration of 15?g?L(-1). Andrews' model gave the best fit with a R (2) value of 0.9993. During the exponential growth phase, the specific growth rate was found to remain fairly constant with respect to time. There was no inhibitory effect due to intracellular product accumulation for all concentrations of glucose. This observation is the first of its kind, as previous studies have reported that increasing accumulation of intracellular carotenoid exerts greater degree of inhibition on growth.     

A model for analyzing growth kinetics of a slowly growing Mycobacterium sp.

This report describes a simple method for quantifying viable mycobacteria and for determining generation time. We used statistical models and computer analysis of growth curves generated for the slowly growing mycobacterium Mycobacterium paratuberculosis under controlled conditions to derive a mathematical formula relating the dependent variable, growth, to the independent variables, log10 number of organisms in the inoculum (inoculum size) and incubation time. Growth was measured by a radiometric method which detects 14CO2 release during metabolism of a 14C-labeled substrate. The radiometric method allowed for early detection of growth and detected as few as three viable bacteria. The coefficient of variation between culture vials inoculated with the same number of M. paratuberculosis was 0.083. Radiometric measurements were highly correlated to spectrophotometric and plate count methods for measuring growth (r = 0.962 and 0.992, respectively). The proportion of the total variability explained by the model in a goodness of fit test was 0.9994. Application of the model to broth cultures provided accurate estimates of the number of M. paratuberculosis (standard error = 0.21, log10 scale) and the growth rate (coefficient of variation, 0.03). Generation time was observed to be dependent upon the number of organisms in the inoculum. The model accurately described all phases of growth of M. paratuberculosis and can likely be applied to other slowly growing microorganisms.     

Temperature-dependent growth kinetics of Escherichia coli ML 30 in glucose-limited continuous culture.

Detailed comparison of growth kinetics at temperatures below and above the optimal temperature was carried out with Escherichia coli ML 30 (DSM 1329) in continuous culture. The culture was grown with glucose as the sole limiting source of carbon and energy (100 mg liter(-1) in feed medium), and the resulting steady-state concentrations of glucose were measured as a function of the dilution rate at 17.4, 28.4, 37, and 40 degrees C. The experimental data could not be described by the conventional Monod equation over the entire temperature range, but an extended form of the Monod model [mu = mu(max) x (s - s(min))/(Ks + s - s(min))], which predicts a finite substrate concentration at 0 growth rate (s(min)), provided a good fit. The two parameters mu(max) and s(min) were temperature dependent, whereas, surprisingly, fitting the model to the experimental data yielded virtually identical Ks values (approximately 33 microg liter(-1)) at all temperatures. A model that describes steady-state glucose concentrations as a function of temperature at constant growth rates is presented. In similar experiments with mixtures of glucose and galactose (1:1 mixture), the two sugars were utilized simultaneously at all temperatures examined, and their steady-state concentrations were reduced compared with to growth with either glucose or galactose alone. The results of laboratory-scale kinetic experiments are discussed with respect to the concentrations observed in natural environments.     

Pilot-scale culture ofCoffea arabica in a novel loop fluidised bed reactor

A novel bubble free loop fluidized bed reactor for plant cell cultures was developed and tested usingCoffea arabica as a model cell line. The effects of main operational parameters like morphology and size of inoculum, oxygen supply as well as recirculation of sparingly soluble gases on cell growth and alkaloid production rates in this reactor were studied and the results were compared with standard shake flask experiments. By on-line monitoring of biomass and oxygen uptake rates the main kinetic parameters for cell growth and alkaloid production were evaluated. It was demonstrated that the novel reactor is easy to run and is particularly adequate for measuring kinetic parameters necessary for scale up.     

Kinetic behavior of mixed populations of activated sludge

The kinetic behavior of heterogeneous microbial populations of sewage origin was studied in a single-stage isothermal continuous flow completely mixed aeration tank. A series of experiments were carried out at various dilution rates using glucose as the growth limiting substrate. The steady-state behavior of the system was observed at each dilution rate and the results were found to fit fairly well with the steady-state equation bayed on the Monod model with an endogenous respiration term included, i.e., μ = μ_mS/(K_s + S) ? K_d. The growth kinetics of cells harvested at steady state for each dilution rate were studied using batch experiments. The multiple response data of the system as functions of time were used to estimate the parameter values in the above kinetic model. It was found that values of the growth parameters changed significantly and systematically with cell population. For example, values of μ_m were high at high dilution rates and low at low dilution rates. It was also found that only those batch growth parameters from cells obtained at fairly high dilution rates are comparable with those estimated by the results of steady-state operations. The results of this investigation suggest that (1) different cell populations pre dominated at different steady-state dilution rates, with high dilution rates resulting in predominantly fast-growing organisms and low dilution rates resulting in predominantly slow-growing cells, and (2) risk exists in any randomly picked batch experiment to predict the steady-state behavior of the system when heterogeneous microbial populations must be used.     

Inhibition Kinetics of Phenol Degradation by Pseudomonas aeruginosa from Continuous Culture and Washout Data

Steady states of a continuous culture with an inhibitory substrate were used to estimate kinetic parameters under substrate limitation (chemostat operation). Pure cultures of an indigenous Pseudomonas aeruginosa were grown in continuous culture on phenol, the sole source of carbon and energy, at dilution rates of 0.010 to 0.20 h^{- 1}. Using different dilution rates, several steady states were investigated and the specific phenol consumption rates were calculated. In addition, phenol degradation was investigated by increasing the dilution rate above the critical dilution rate (washout cultivation). The results showed that the specific phenol consumption rate increased with increased dilution rate at steady state and that the degradation by Pseudomonas aeruginosa can be described by simple substrate inhibition kinetics under substrate limitation but cannot be described by simple substrate inhibition kinetics under washout cultivation. Fitting of the steady-state data from continuous cultivation to various inhibition models resulted in the best fit for the Yano and Koga kinetic inhibition model. The r_{s max} value of 0.278 mg/mg/h obtained from the Yano and Koga equation was comparable to the experimentally calculated r_{s max} value of 0.283 mg/mg/h obtained under washout cultivation.     

A metabolic model of the biological phosphorus removal process: II. Validation during start-up conditions

A metabolic model of the biological phosphorus removal process has been developed and validated previously for complex conversions during the process under anaerobic and aerobic conditions at different growth rates in sequencing batch reactors in steady state. For additional validation of the metabolic model, the model was applied to the dynamic conditions which occur during the start-up phase of the biological P removal in the presence and absence of non-polyP heterotrophic microorganisms. In a laboratory scale sequencing batch reactor, experiments were performed to examine the enrichment of the population with polyphosphate organisms during the start-up and the subsequent shift from non-polyP, heterotrophic organisms to polyP organisms in the sludge. The effect of different influent loading patterns for acetate and phosphate was studied. In these experiments, the maximal growth rate of the polyP organisms and the behavior of the internal storage compounds could be derived. The metabolic model was capable of describing the experimental results, without the need to adjust the kinetic or stoichiometric parameters obtained under steady state conditions. (c) 1995 John Wiley & Sons, Inc.     

Escherichia coli DNA distributions measured by flow cytometry and compared with theoretical computer simulations.

A computer simulation routine has been made to calculate the DNA distributions of exponentially growing cultures of Escherichia coli. Calculations were based on a previously published model (S. Cooper and C.E. Helmstetter, J. Mol. Biol. 31:519-540, 1968). Simulated distributions were compared with experimental DNA distributions (histograms) recorded by flow cytometry. Cell cycle parameters were determined by varying the parameters to find the best fit of theoretical to experimental histograms. A culture of E. coli B/r A with a doubling time of 27 min was found to have a DNA replication period (C) of 43 min and an average postreplication period (D) of 22 to 23 min. Similar cell cycle parameters were found for a 60-min B/r A culture. Initiations of DNA replication at multiple origins in one and the same cell were shown to be essentially synchronous. A slowly growing B/r A culture (doubling time, 5.5 h) had an average prereplication period (B) of 2.3 h; C = 2.4 h and D = 0.8 h. It was concluded the the C period has a constant duration of 43 min (at 37 degrees C) at fast growth rates (doubling times, less than 1 h) but increases at slow growth rates. Thus, our results obtained with unperturbed exponential cultures in steady state support the model of Cooper and Helmstetter which was based on data obtained with synchronized cells.     

A model for analyzing growth kinetics of a slowly growing Mycobacterium sp

This report describes a simple method for quantifying viable mycobacteria and for determining generation time. We used statistical models and computer analysis of growth curves generated for the slowly growing mycobacterium Mycobacterium paratuberculosis under controlled conditions to derive a mathematical formula relating the dependent variable, growth, to the independent variables, log10 number of organisms in the inoculum (inoculum size) and incubation time. Growth was measured by a radiometric method which detects 14CO2 release during metabolism of a 14C-labeled substrate. The radiometric method allowed for early detection of growth and detected as few as three viable bacteria. The coefficient of variation between culture vials inoculated with the same number of M. paratuberculosis was 0.083. Radiometric measurements were highly correlated to spectrophotometric and plate count methods for measuring growth (r = 0.962 and 0.992, respectively). The proportion of the total variability explained by the model in a goodness of fit test was 0.9994. Application of the model to broth cultures provided accurate estimates of the number of M. paratuberculosis (standard error = 0.21, log10 scale) and the growth rate (coefficient of variation, 0.03). Generation time was observed to be dependent upon the number of organisms in the inoculum. The model accurately described all phases of growth of M. paratuberculosis and can likely be applied to other slowly growing microorganisms.     

Growth Kinetics and Toxicity of <Emphasis Type="Italic">Enterobacter cloacae</Emphasis> Grown on Linear Alkylbenzene Sulfonate as Sole Carbon Source

A successful attempt was made to isolate linear alkylbenzene sulfonate (LAS)-degrading bacteria from soil irrigated with wastewater. The isolated bacteria were able to use LAS as sole carbon and energy source. Maximum growth rates on LAS reached only 0.27 h(-1). 16S-rRNA sequencing and fatty-acid analysis placed the bacteria in the genus Enterobacter cloacae. The growth curves of E. cloacae both in the presence of and the absence of LAS were monitored using measurements of optical density at 600 nm in two different media, nutrient broth and M9 minimal medium, and were modeled mathematically. Growth in NB fit the Riccati and Voltera models, indicating that LAS is not toxic to E. cloacae cells. However, growth of E. cloacae in LAS-containing MM fit the Riccati and Voltera models, whereas growth in LAS-free MM fit the Riccati model only. Furthermore, the kinetic data shown were modeled by Monod's, Andrew's, and Tessier's specific growth rate equations, coupled with the rate of consumption of different concentrations of LAS as sole carbon and energy source, and we determined that Andrew's model best fit these data adequately as a result of the cell-inhibitory effect.     

Kinetics of biodegradation of binary and ternary mixtures of PAHs

The kinetics of biodegradation of mixtures of polycyclic aromatic hydrocarbons (PAHs) by Sphingomonas paucimobilis strain EPA505 were investigated. The investigation focused on three- and four-ring PAHs, specifically 2-methylphenanthrene, fluoranthene, and pyrene. Uptake rates in aerobic batch suspended cultivations were measured for the individual PAHs and their binary and ternary mixtures. It was observed that kinetics were influenced by the mixture composition and the kinetic properties of the components. A material balance equation containing the Monod model was numerically fitted to uptake data to determine extant kinetic parameters for the individual PAHs. Similarly, equations containing kinetic interaction models derived from enzyme kinetics were fitted to the uptake data obtained from experiments with binary and ternary mixtures. The investigation considered the following interaction types: no-interaction (Monod), pure competitive interaction, noncompetitive or mixed-type interaction, uncompetitive inhibition, and nonspecific interaction based on pure competition (SKIP). Model fit was evaluated based on probabilistic and statistical criteria and inferences were reached about underlying interaction mechanisms based on model fit. Mixture kinetics were most adequately simulated by the pure competitive interaction model with mutual substrate exclusivity. This model is fully predictive, relying only on parameters determined in the sole-PAH experiments. It was shown that for low percent inhibition values and with limited data, pure competitive interaction kinetics may not be evident, resembling no-interaction kinetics. This study is a reasonable starting point for understanding and modeling biodegradation of complex PAH mixtures in engineered and natural systems.     

Multisubstrate biodegradation kinetics of naphthalene, phenanthrene, and pyrene mixtures.

Biodegradation kinetics of naphthalene, phenanthrene and pyrene were studied in sole-substrate systems, and in binary and ternary mixtures to examine substrate interactions. The experiments were conducted in aerobic batch aqueous systems inoculated with a mixed culture that had been isolated from soils contaminated with polycyclic aromatic hydrocarbons (PAHs). Monod kinetic parameters and yield coefficients for the individual compounds were estimated from substrate depletion and CO(2) evolution rate data in sole-substrate experiments. In all three binary mixture experiments, biodegradation kinetics were comparable to the sole-substrate kinetics. In the ternary mixture, biodegradation of naphthalene was inhibited and the biodegradation rates of phenanthrene and pyrene were enhanced. A multisubstrate form of the Monod kinetic model was found to adequately predict substrate interactions in the binary and ternary mixtures using only the parameters derived from sole-substrate experiments. Numerical simulations of biomass growth kinetics explain the observed range of behaviors in PAH mixtures. In general, the biodegradation rates of the more degradable and abundant compounds are reduced due to competitive inhibition, but enhanced biodegradation of the more recalcitrant PAHs occurs due to simultaneous biomass growth on multiple substrates. In PAH-contaminated environments, substrate interactions may be very large due to additive effects from the large number of compounds present.     

Growth models of cultures with two liquid phases. VI. Parameter estimation and statistical analysis

Parameter estimation studies have been conducted employing mathematical models developed previously by the investigators and experimental data collected by the last author. A batch fermentation process in which Candida lipolytica were cultured on n-hexadecane dissolved in dewaxed gas oil was employed to obtain the experimental data. The kinetic data from a number of batch experiments conducted at different initial substrate concentrations and different dispersed phase volume fractions were analyzed assuming that, the basic model parameters (maximum specific growth rate, saturation constant, substrate phase equilibrium constant, adsorption constant, desorption constant, etc.) did not change from experiment to experiment. The Gauss-Newton method with modification by Greenstadt, Eisenpress, Bard, and Carroll was used to minimize the conventional sum of squares criterion on the IBM 300/50 computer. The individual confidence intervals were obtained for each individual parameter. Tin- models were compared employing the F-test for equality of variances and an analysis of residuals. For the two best models, the estimated parameter values were compared with available experimental information. The results showed good agreement between the experimental data and the values predicted by the mathematical models. The results presented in this work did suggest that growth on small segregated drops may be more important than continuous phase growth on dissolved substrate.     

Continuous cultivation of fission yeast: Analysis of single-cell protein synthesis kinetics

A fundamental problem in microbial reactor analysis is identification of the relationship between environment and individual cell metabolic activity. Population balance equations provide a link between experimental measurements of composition frequency functions in microbial populations on the one hand and macromolecular synthesis kinetics and cell division control parameters for single cells on the other. Flow microfluorometry measurements of frequency functions for single-cell protein content in Schizosaccharomyces pombe in balanced exponential growth have been analyzed by two different methods. One approach utilizes the integrated form of the population balance equation known as the Collins-Richmond equation, and the other method involves optimization of parameters in assumed kinetic and cell division functional forms in order to best fit measured frequency functions with corresponding model solutions. Both data interpretation techniques indicate that rates of protein synthesis increase most in small protein content cells as the population specific growth rate increases, leading to parabolic single-cell protein synthesis kinetics at large specific growth rates. Utilization of frequency function data for an asynchronous population is shown in this case to be a far more sensitive method for determination of single-cell kinetics than is monitoring the metabolic dynamics of a single cell or, equivalently, synchronous culture analyses.     

Model-based analysis of anaerobic acetate uptake by a mixed culture of polyphosphate-accumulating and glycogen-accumulating organisms

An increasing number of studies shows that the glycogen-accumulating organisms (GAOs) can survive and may indeed proliferate under the alternating anaerobic/aerobic conditions found in EBPR systems, thus forming a strong competitor of the polyphosphate-accumulating organisms (PAOs). Understanding their behaviors in a mixed PAO and GAO culture under various operational conditions is essential for developing operating strategies that disadvantage the growth of this group of unwanted organisms. A model-based data analysis method is developed in this paper for the study of the anaerobic PAO and GAO activities in a mixed PAO and GAO culture. The method primarily makes use of the hydrogen ion production rate and the carbon dioxide transfer rate resulting from the acetate uptake processes by PAOs and GAOs, measured with a recently developed titration and off-gas analysis (TOGA) sensor. The method is demonstrated using the data from a laboratory-scale sequencing batch reactor (SBR) operated under alternating anaerobic and aerobic conditions. The data analysis using the proposed method strongly indicates a coexistence of PAOs and GAOs in the system, which was independently confirmed by fluorescent in situ hybridization (FISH) measurement. The model-based analysis also allowed the identification of the respective acetate uptake rates by PAOs and GAOs, along with a number of kinetic and stoichiometric parameters involved in the PAO and GAO models. The excellent fit between the model predictions and the experimental data not involved in parameter identification shows that the parameter values found are reliable and accurate. It also demonstrates that the current anaerobic PAO and GAO models are able to accurately characterize the PAO/GAO mixed culture obtained in this study. This is of major importance as no pure culture of either PAOs or GAOs has been reported to date, and hence the current PAO and GAO models were developed for the interpretation of experimental results of mixed cultures. The proposed method is readily applicable for detailed investigations of the competition between PAOs and GAOs in enriched cultures. However, the fermentation of organic substrates carried out by ordinary heterotrophs needs to be accounted for when the method is applied to the study of PAO and GAO competition in full-scale sludges.     

Oxidation of an inhibitory substrate by washed cells (oxidation of phenol by Pseudomonas putida)

The specific uptake rate of phenol by washed cells of Pseudomonas putida grown on phenol in steady-state continuous culture at various dilution rates was studied. The Monod-Haldane-type equation was applied to fit the data and the best kinetic parameters were determined by nonlinear least-squares techniques. The values of the kinetic parameters were found to increase monotonically with the phenol concentration in the original chemostat. The relations between the values of kinetic parameters and phenol concentration in the chemostat were described by empirical equations. Then the equation governing the instant uptake of phenol by microorganisms in chemostat in the high conversion range of phenol was proposed. This equation together with the mass balance equations can be used to determine the stability range of continuous stirred tank biochemical reactors (CSTBR) utilizing phenol.     

Models for the kinetics of biodegradation of organic compounds not supporting growth.

We developed 12 models of kinetics to describe the metabolism of organic substrates that are not supporting bacterial growth. These models can be used to describe the biodegradation of organic compounds that are not supporting growth when the responsible populations are growing logistically, logarithmically, or linearly or are not increasing in numbers. Nonlinear regression analysis was used to fit patterns of mineralization by two bacteria to these kinetic models. Pseudomonas acidovorans mineralized 1 ng of phenol per ml while growing exponentially at the expense of uncharacterized organic carbon in a synthetic medium. Phenol at a concentration of 1 ng/ml did not affect the growth of P. acidovorans. These data were best fit by the model that incorporates the equation for logarithmic growth and assumes a concentration of test substrate well below its Km value. In the absence of a second substrate, glucose at concentrations below those supporting growth was mineralized by Salmonella typhimurium in a manner best described by pseudo first-order kinetics. In the presence of different concentrations of arabinose, however, the kinetics of glucose mineralization by S. typhimurium reflected linear, logistic, or logarithmic growth of the population on arabinose. We conclude that the kinetics of mineralization of organic compounds at concentrations too low to support growth are best described either by the first-order model or by models that incorporate expressions for the kinetics of growth of the metabolizing population on other substrates. When growth is at the expense of other substrates, the kinetics observed reflect such growth, as well as the concentration of the substrate of interest.(ABSTRACT TRUNCATED AT 250 WORDS)